Technical Glossary

Excess death rate (EDR)

The excess death rate for a group of persons of a given age is the difference between the group's death rate and that of a suitable reference group. For example, the mortality rate for U.S. males at age 40 is 0.00316, or 3.16 deaths per thousand person-years (Table 1). If a study shows that the mortality rate for 40-year-old U.S. males who have some chronic disease X is 7.48 per thousand person-years, then the EDR for condition X is 7.48 - 3.16 = 4.32 per thousand.

Expected present value (EPV)

Future payments are generally discounted: a dollar to be paid in the future is worth less than a dollar at present. That is, the present value of $1,000 per year for 50 years is worth less than $50,000 today. Suppose that a man's life expectancy at his current age is 50 additional years, and that he is promised annual payments of $1,000 for as long as he shall live. He may ultimately receive more or less than $50,000, but on average will receive $50,000 over his life span. But, the present value of his total -- again, on average -- will be less than $50,000. This latter amount is known as the expected present value. See the separate section on discounted cost of future care and expenses.

Life expectancy

The life expectancy of a cohort of a given age is the arithmetic mean of the actual survival times of all the individuals. For example, consider a cohort of just five individuals all born on the same day. If they live 10, 20, 50, 60, and 80 years, respectively, the life expectancy of the cohort is (10+20+50+60+80)/5 = 44 years. Note that three of the individuals lived to age 40 and beyond; at age 40 their life expectancy would be (10 + 20 + 40)/3 = 23.3 additional years.

Median survival time

The median survival time is the middle survival time for the cohort if the survival times of are arranged from smallest to largest. For example, consider a cohort of just five individuals all born on the same day. If the 5 individuals lived for 10, 20, 50, 60, and 80 years, respectively, then the median survival time would be 50 years. The survivors at age 40 have medial survival time of 20 additional years. In Table 1 the median survival time for the cohort of 100,000 individuals at birth is between 75 and 76 years, the time at which l(x) has diminished from 100,000 to 50,000. Compare to the life expectancy of the entire cohort, 71.8 years.

Mortality rate

The mortality rate for a cohort during a given time interval is the number of deaths occurring during the interval divided by the total exposure, or person-time at risk, during that interval. For example, consider a cohort of 5 individuals followed for one year. If one person died three months into the year (one-fourth of a person-year at risk of death), two people died six months into the year, and the remaining two people lived to the end of the year, then the total exposure for the year is 1/4 + 2(1/2) + 2(1) = 3.25 person-years. The total number of deaths is 3. The mortality rate is m = 3/3.25 = 0.923. The general formula for the mortality rate at age x in a life table is m(x) = d(x)/L(x).

Mortality risk (or mortality probability)

The mortality risk for a cohort over a given time interval is the number of people dying in the interval divided by the number alive at the beginning of the interval. For a given age in a life table, this is q(x) = d(x)/l(x).

Multiplier

The multiplier is the expected present value (for a given discount rate) of a stream of payments of 1 unit per year for the rest of an individual's survival time. See the separate section on discounted cost of future care and expenses.

Relative risk (RR)

The relative risk of death for group A relative to group B is the ratio of the mortality risks. Strictly this refers to the ratio of the mortality rates (m), but it is approximately equal to the ratio of the mortality probabilities (q).

Survival time

The survival time of an individual is the actual number of years they survive beyond a given age or point in time.